You are not necessarily doing anything wrong. Swelling in the hands is a very common problem for many runners, especially on longer runs. There are few potential causes of the swelling which probably together contribute to the problem in most people.
First, there is the swinging action of the arms, which actually drives liquid down into the hands and fingers. This is made worse by the fact that blood flow to the hands is increased while running as the body attempts to supply necessary blood to active muscle groups. Dehydration or loss of electrolytes during a run is the third factor that leads to leaking of fluid out of the blood vessels and into the tissues.
In order to prevent hand swelling while running, make sure that you are well hydrated before your run. Also drink lots of liquids during the run and, if you are going on a long run, make sure to take electrolyte replacements as well. Avoid running in the heat, as this tends to make the swelling problem worse, and try to run with your hands elevated above your heart rather than down at your sides.
In any case, you should discuss this with your family doctor
. He or she can give you a full workup and make sure there is not a more serious problem causing your hand swelling. Good luck!